Answered: Question about being dq'd if a stack of cones falls on you.

Watch the last 6 seconds of this video Vex in the zone stacking test - YouTube
Can I be disqualified due to possessing multiple cones due to this?

There would not be an immediate penalty, however the Robot would be responsible for removing the Cones in a timely fashion. If they cannot, they could be disqualified if it is determined that the possession was Match Affecting.